1. Field of the Invention
The present invention relates to a control system for executing feedback control.
2. Description of the Related Art
For example, in a photolithography process or CVD (Chemical Vapor Deposition) process in the manufacture of semiconductor devices, a semiconductor wafer as an object is treated while controlling the temperature of the semiconductor wafer to a predetermined value. In general, temperature control of this type adopts feedback control.
A typical feedback control method for the wafer temperature control is based on a PID controller. The PID controller is constituted by combining a proportional action (P), an integral action (I), and a derivative action (D), and calculates a manipulated variable u from the following equation on the basis of a deviation e between a wafer temperature detection value and a wafer temperature preset value: EQU u=Kp.multidot.e+KI.intg.e.multidot.dt+KD.multidot.de/dt (1)
where the coefficients KP, KI, and KD respectively represent the sensitivities of the proportional, integral, and derivative actions, and are set according to the characteristics of the corresponding control system.
The PID controller adjusts an energy supply amount to a wafer heating arrangement on the basis of the manipulative variable u calculated from equation (1), so that the deviation e becomes zero, i.e., a control variable is caused to coincide with a target value.
However, the wafer temperature control suffers from temporal and positional deviations between wafer temperature detection and a wafer temperature to be actually controlled. More specifically, when the temperature of a wafer in a process is detected, since a thermal sensor such as a thermocoupler cannot be attached to a to-be-treated surface (upper surface) of the wafer, the thermal sensor is attached to the peripheral edge portion of the lower surface of the wafer to detect the wafer temperature. For this reason, the wafer temperature detection value obtained by the thermal sensor represents the temperature of the peripheral edge portion of the lower surface of the wafer, and does not represent the temperature of the to-be-treated surface (upper surface) of the wafer. Therefore, in the control method of the PID controller, since control for feeding back such a wafer temperature detection value, and causing it to coincide with a preset value is executed, it is difficult to cause the temperature of the to-be-treated surface (upper surface) of the wafer to coincide with a desired value.